High School

Which expression is equivalent to \(-5(x + 2)(2x - 1)(x + 1)\)?

A. \(-10x^3 + 25x^2 - 5x + 10\)

B. \(-10x^3 - 25x^2 - 5x - 2\)

C. \(2x^3 + 25x^2 - 5x - 10\)

D. \(2x^3 - 25x^2 - 5x - 2\)

Answer :

Final answer:

The expression -5(x + 2)(2x - 1)(x + 1) is equivalent to -10x³ - 25x² - 5x - 2.

Explanation:

The expression that is equivalent to -5(x + 2)(2x - 1)(x + 1) is b. -10x³ - 25x² - 5x - 2.

To simplify the expression, distribute the -5 to each term inside the parentheses:
-5x - 10
-10x² + 5x
-5x - 5

Then combine like terms:
-10x³ - 10x² + 5x² - 5x - 5

Finally, arrange the terms in descending order of degree:
-10x³ - 25x² - 5x - 2

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